Method for automated steering of a motor vehicle

ABSTRACT

A method for automated steering of a motor vehicle including wheels at least two of which are steered wheels. The method comprising: acquiring parameters relating to a path for avoidance of an obstacle by the motor vehicle, and calculating, by a computer, a first steering setpoint for a steering actuator for the steered wheels and a second steering setpoint for at least one actuator for differential braking of the wheels, depending on the parameters. The first and second steering setpoints are each determined by a controller respecting a model that limits setpoint variation and/or range.

TECHNICAL FIELD OF THE INVENTION

The present invention relates in general to automation of the followingof trajectories of motor vehicles.

It has a particularly advantageous application in the context of aidsfor the driving of motor vehicles.

It more particularly relates to a process for automated piloting of amotor vehicle, allowing this vehicle to follow an obstacle evasiontrajectory.

It also relates to a motor vehicle equipped with a computer adapted tocarry out this process.

PRIOR ART

With a view to the safety of motor vehicles, they are currently equippedwith driving assistance systems or self-driving systems.

Among these systems, automatic emergency braking systems (more commonlyknown by the abbreviation AEB) are known, which are designed to avoidany collision with obstacles located on the path taken by the vehicle.These systems are designed to detect an obstacle on the road and, inthis situation, to intervene on the conventional braking system of themotor vehicle.

There are, however, situations in which these emergency braking systemsdo not make it possible to avoid a collision or cannot be used (forexample if another vehicle is following too close behind the motorvehicle).

For these situations, automatic evasion systems (more commonly known bythe abbreviation AES for “Automatic Evasive Steering” or “AutomaticEmergency Steering”) have been developed, which make it possible toavoid the obstacle by diverting the vehicle from its trajectory, byintervening either on the steering of the vehicle or on thedifferential-braking system of the vehicle.

An obstacle evasion process is also known from the documentWO2020099098, in which the steering-angle and differential-brakingsystems are commanded in combination in order to manage the evasivetrajectory. The steering-angle system is used to ensure good stabilityat medium speeds, while the braking system is used at high speeds.

It sometimes happens that this AES system imposes on the vehicle atrajectory that is at the limit in terms of controllability, which doesnot allow the driver to take over the driving of the vehicle again infull capacity.

SUMMARY OF THE INVENTION

In order to overcome the aforementioned drawback of the prior art, thepresent invention proposes to use a mixed controller which intervenesboth on the steering angle of the steered wheels and on the differentialbraking of the right and left wheels of the vehicle, and which isadapted to create a piloting setpoint that limits the amplitude and/orthe rate of the steering change imposed on the motor vehicle.

More particularly, the invention provides a process for automatedpiloting of a motor vehicle, having steps of:

-   -   acquiring parameters relating to a trajectory for the motor        vehicle to avoid an obstacle, and of    -   calculating by a computer a first piloting setpoint of a        steering-angle actuator of the steered wheels and a second        piloting setpoint of at least one differential-braking actuator        of the wheels, as a function of said parameters,        wherein the first piloting setpoint and the second piloting        setpoint are each determined by means of a control that        satisfies a setpoint amplitude and/or variation limiting model.

Thus, by virtue of the invention, it is possible to use a mixed controllaw that intervenes on the steering angle and on the differentialbraking so that the vehicle follows an obstacle evasion trajectory. Thiscontrol law is optimized in order to ensure a control of the vehiclewhich performs well (that is to say it is rapid enough to ensure theobstacle evasion) and is stable and robust.

For this purpose, the invention proposes to apply constraints in termsof amplitude and rate (that is to say of setpoint variation). Itpreferably furthermore proposes to inhibit the calculation of thepiloting setpoints, when this proves necessary, that is to say to stopthe control of the brakes or of the steering angle when the conditionsso require. This stopping may be temporary or permanent, until a newactivation of the AES system.

Other advantageous and nonlimiting characteristics of the processaccording to the invention, taken individually or in any technicallyfeasible combinations, are as follows:

-   -   the first piloting setpoint and/or the second piloting setpoint        is determined by means of a controller that satisfies a setpoint        amplitude and variation limiting model;    -   the first piloting setpoint and the second piloting setpoint are        determined as a function of a coefficient that fixes the        contribution of each actuator (in the piloting of the steering        of the vehicle), said coefficient being calculated as a function        of a yaw velocity of the motor vehicle and a torque applied by        the driver to the steering wheel of the motor vehicle;    -   said coefficient also being calculated as a function of a        parameter, the value of which varies according to whether or not        the first piloting setpoint is saturated (that is to say        according to whether or not it is limited by the controller);    -   the coefficient is calculated so that the second piloting        setpoint is zero if the absolute value of a torque applied by a        driver to a steering wheel of the motor vehicle exceeds a        predetermined threshold;    -   the coefficient is calculated so that only the steering-angle        actuator of the steered wheels is used when the yaw velocity of        the vehicle is greater than a control threshold and/or when the        first piloting setpoint on its own makes it possible to        stabilize the motor vehicle;    -   the coefficient is calculated so that the steering-angle        actuator of the steered wheels and the differential-braking        actuator of the wheels are otherwise used in combination;    -   the coefficient is calculated so as to vary continuously as a        function of time;    -   provision is made to interrupt (preferably permanently) the        determination of the first piloting setpoint when the absolute        value of a torque applied by a driver to a steering wheel of the        motor vehicle exceeds a predetermined threshold;    -   provision is made to interrupt (temporarily or permanently) the        determination of the second piloting setpoint when the absolute        value of a torque applied by a driver to a steering wheel of the        motor vehicle exceeds another predetermined threshold;    -   the controller that makes it possible to determine the second        piloting setpoint satisfies an amplitude limiting model, so that        the second piloting setpoint remains less than or equal to a        limit value;    -   said limit is determined as a function of the velocity of the        vehicle and the yaw velocity of the motor vehicle;    -   in order to calculate the first piloting setpoint, provision is        made to determine a first non-saturated setpoint and to deduce        the first setpoint therefrom by means of a closed-loop        pseudo-controller having a direct-chain transfer function that        comprises a function of the hyperbolic tangent type of the        deviation between the first non-saturated setpoint and the first        setpoint;    -   in order to calculate the second setpoint, provision is made to        determine a second non-saturated setpoint and to deduce a second        semi-saturated setpoint therefrom by means of a closed-loop        pseudo-controller having a direct-chain transfer function that        comprises a function of the hyperbolic tangent type of the        deviation between the second non-saturated setpoint and the        second semi-saturated setpoint, then to use another closed-loop        pseudo-controller, which provides the second setpoint as output        and the direct-chain transfer function of which comprises a        function of the hyperbolic tangent type of the deviation between        the second semi-saturated setpoint and said second setpoint.

The invention also provides a method for creating controllers with aview to their use in a piloting process as mentioned above, whereinprovision is made:

-   -   to acquire a behavioral matrix model of the apparatus,    -   to determine at least some of the coefficients of the matrices        of the behavioral matrix model,    -   to deduce two controllers therefrom, each of which satisfies the        following of the trajectory to be taken, namely a piloting        setpoint amplitude limiting model and/or a piloting setpoint        variation limiting model.

The invention also provides a motor vehicle comprising a steering-angleactuator of the steered wheels, a differential-braking actuator of thewheels, and a computer for piloting said actuators, which is programmedin order to carry out a process as mentioned above.

The various characteristics, variants and embodiments of the inventionmay of course be combined with one another in various combinations solong as they are not mutually incompatible or exclusive.

DETAILED DESCRIPTION OF THE INVENTION

The description that follows with reference to the appended drawings,which are given by way of nonlimiting examples, will clearly explainwhat the invention consists in and how it may be carried out.

In the appended drawings:

FIG. 1 is a schematic view from above of a motor vehicle traveling on aroad, on which the trajectory that this vehicle is meant to take isrepresented;

FIG. 2 is a schematic perspective view of the motor vehicle of FIG. 1 ,represented in four successive positions that lie along a trajectory foravoiding an obstacle;

FIG. 3 is a diagram illustrating a closed-loop transfer function used toimplement a saturation function of the steering angle of the wheels ofthe vehicle;

FIG. 4 is a diagram illustrating closed-loop transfer functions used toimplement saturation functions of the differential braking of the wheelsof the vehicle;

FIG. 5 is a diagram illustrating steps of an operation of determiningvalues that can be used in a procedure of piloting a motor vehicleaccording to the invention;

FIG. 6 is a graph illustrating the various saturation and inhibitionfunctions that can be used in the scope of this procedure of pilotingthe motor vehicle.

FIG. 1 represents a motor vehicle 10 which, in the conventional way,comprises a chassis that delimits a passenger compartment, two steeredfront wheels 11 and two non-steered rear wheels 12. As a variant, thesetwo rear wheels could also be steered, although this would requireadaptation of the command law described below.

This motor vehicle 10 has a conventional steering system making itpossible to intervene on the orientation of the front wheels 11 so as tobe able to turn the vehicle. This conventional steering system has inparticular a steering wheel connected to tie rods in order to make thefront wheels 11 pivot. In the example considered, it also has anactuator 31 (represented in FIG. 6 ) making it possible to intervene onthe orientation of the front wheels as a function of the orientation ofthe steering wheel and/or as a function of a request received from acomputer 13.

In addition, this motor vehicle has a differential-braking system makingit possible to intervene directly on the front wheels 11 (and on therear wheels 12) so as to decelerate the motor vehicle while making itturn. This differential-braking system comprises, for example, a piloteddifferential or electric motors, which are positioned at the wheels ofthe vehicle, or brake calipers that are piloted independently of oneanother. It also has at least one actuator 32 (represented in FIG. 6 ),which is designed to intervene directly on the rotational speeds of thewheels as a function of a request received from a computer 13. It willbe assumed here that it has a plurality of actuators 32.

The computer 13 is then intended to pilot the assisted-steering actuator31 and the actuators 32 of the differential-braking system as a functionof the traffic conditions encountered. For this purpose, it has at leastone processor, at least one memory, and an input and output interface.

By virtue of its interface, the computer 13 is adapted to receive inputsignals coming from various sensors.

Among these sensors, the following are for example provided:

-   -   a device, such as a front camera, making it possible to identify        the position of the vehicle in relation to its road lane,    -   a device, such as a RADAR or LIDAR remote detector, making it        possible to detect an obstacle 20 lying on the trajectory of the        motor vehicle 10 (FIG. 2 ),    -   at least one lateral detection device, such as a RADAR or LIDAR,        making it possible to observe the environment to the sides of        the vehicle,    -   a device, such as a gyrometer, making it possible to determine        the yaw rotation velocity (about a vertical axis) of the motor        vehicle 10,    -   a sensor of the position and angular velocity of the steering        wheel, and    -   a sensor of the torque applied by the driver to the steering        wheel.

By virtue of its interface, the computer 13 is adapted to transmit onesetpoint to the assisted-steering actuator 31 and another setpoint tothe actuators 32 of the differential-braking system.

It also makes it possible to force the vehicle to follow a trajectory T0for avoiding the obstacle 20 (see FIG. 2 ).

By virtue of its memory, the computer 13 stores data used in the scopeof the process described below.

In particular, it stores application software consisting of computerprograms comprising instructions, the execution of which by theprocessor makes it possible for the process described below to becarried out by the computer.

Before describing this process, the different variables that will beused may be introduced, some of which are illustrated in FIG. 1 .

The total mass of the motor vehicle will be denoted “m”, and will beexpressed in kg.

The inertia of the motor vehicle about a vertical axis passing throughits center of gravity CG will be denoted “J” or “I_(z)”, and will beexpressed in N.m.

The distance between the center of gravity CG and the front axle of thevehicle will be denoted “If”, and will be expressed in meters.

The distance between the center of gravity CG and the rear axle will bedenoted “I_(r)”, and will be expressed in meters.

The cornering stiffness coefficient of the front wheels will be denoted“C_(f)”, and will be expressed in N/rad.

The cornering stiffness coefficient of the rear wheels will be denoted“C_(r)”, and will be expressed in N/rad.

These cornering stiffness coefficients of the wheels are concepts wellknown to a person skilled in the art. By way of example, the corneringstiffness coefficient of the front wheels is thus that which allows theequation F_(f)=2·C_(f)·α_(f) to be written, with F_(f) the lateral slipforce of the front wheels and α_(f) the drift angle of the front wheels.

The steering angle that the steered front wheels make with thelongitudinal axis A1 of the motor vehicle 10 will be denoted “δ”, andwill be expressed in rad.

The variable δ_(ref), expressed in rad, will denote the saturatedsteering-angle setpoint, as will be transmitted to the assisted-steeringactuator.

The variable δ_(K), expressed in rad, will denote the non-saturatedsteering-angle setpoint. At this stage, it may only be stated that theconcept of saturation will be linked with limits of value or valuevariation.

The yaw velocity of the vehicle (about the vertical axis passing throughits center of gravity CG) will be denoted “r”, and will be expressed inrad/s.

The relative heading angle between the longitudinal axis A1 of thevehicle and the tangent to the evasion trajectory T0 (desired trajectoryof the vehicle) will be denoted “Ψ_(L)”, and will be expressed in rad.

The lateral deviation between the longitudinal axis A1 of the motorvehicle 10 (passing through the center of gravity CG) and the evasiontrajectory T0, at a sighting distance “Is” lying in front of thevehicle, will be denoted “y_(L)”, and will be expressed in meters.

The setpoint of lateral deviation between the longitudinal axis A1 ofthe motor vehicle 10 (passing through the center of gravity CG) and theevasion trajectory T0, at a sighting distance “Is” lying in front of thevehicle, will be denoted “y_(L-ref)”, and will be expressed in meters.

The trajectory following error will be denoted “e_(yL)”, and will beexpressed in meters. It will be equal to the difference between thelateral deviation setpoint y_(L-ref) and the lateral deviation y_(L).

The aforementioned sighting distance “Is” will be measured from thecenter of gravity CG, and will be expressed in meters.

The drift angle of the motor vehicle 10 (the angle which the velocityvector of the motor vehicle makes with its longitudinal axis A1) will bedenoted “β”, and will be expressed in rad.

The velocity of the motor vehicle along the longitudinal axis A1 will bedenoted “V”, and will be expressed in m/s.

The constant “g” will be the acceleration due to gravity, expressed inm·s⁻².

The average curvature of the road level with the motor vehicle willdenoted ρ_(ref), and will be expressed in m⁻¹.

The setpoint of yaw moment to be applied by virtue of thedifferential-braking means will be denoted “M_(z_ref)”, and will beexpressed in N.m.

The constants “ξ” and “ω” will represent dynamic characteristics of thesteering angle of the front wheels of the vehicle.

The constant “ω_(f)” will for its part represent a dynamiccharacteristic of an arbitrary bounded perturbation “w” applied to thevehicle.

The steering-angle velocity will denote the steering angular velocity ofthe steered front wheels.

As an assumption, the road on which the motor vehicle is moving ispresumed to be straight and flat. They extend along a principal axis.

Before describing the process that will be performed by the computer 13in order to carry out the invention, in a first part of this explanationthe constraints that are selected in order to ensure effective pilotingof the motor vehicle may be summarized, then the calculations that havemade it possible to achieve the controllers allowing the invention to beimplemented may be described, so as to understand clearly where thesecalculations come from and on what they are based.

In the part X1 of FIG. 6 , the procedure of calculating the saturatedsteering-angle setpoint δ_(ref) to be transmitted to theassisted-steering actuator 31, and the yaw setpoint moment M_(z_ref) tobe transmitted to the differential-braking actuators 32, has beenmodeled.

The part X2 is in turn given over to schematizing the way in which thesesetpoints interact with the actuators 31, 32.

This second part X2 shows the constraints that are applied to theaforementioned setpoints so as to ensure stability and controllabilityof the vehicle by the driver when a driving assistance system of the AEStype is activated.

The first constraint Z5, which is applied to the saturatedsteering-angle setpoint δ_(ref), is a velocity saturation. It is moreprecisely a limitation of the steering-angle velocity of the vehicle.The steering angular velocity threshold used is denoted υ.

This first constraint, by virtue of a feedback loop that provides thecurrent steering angle δ__(meas), and a controller K_(DAE), makes itpossible to obtain a provisional engine torque.

The second constraint Z7, which is applied to the output of thecontroller K_(DAE), is an amplitude saturation. It is more precisely alimitation of the absolute value of the aforementioned provisionalengine torque. The engine torque threshold used is denotedne_(EPS_saturation_1).

The block Z6 illustrates a first mechanism for inhibiting the regulationof the saturated steering-angle setpoint δ_(ref). This first mechanismis intended to block the regulation, and therefore the calculation ofany engine torque to be provided to the assisted-steering actuator 31,when the absolute value of the torque exerted by the driver on thesteering wheel exceeds a threshold denoted T_(Driver_δ) ^(ctrl).

The third constraint Z8, which is applied to the yaw-moment setpointM_(z_ref), is an amplitude saturation. It is more precisely a limitationof the value of this yaw-moment setpoint M_(z_ref), the aim of which isto prevent the differential braking from being too great and preventingsatisfactory stability and controllability of the vehicle from beingensured. The yaw moment threshold used is referred to as limitM_(z_max).

The limit M_(z_max) used for this saturation will preferably bevariable. It will be calculated (in block Z10) as a function of at leastthe yaw velocity r and the velocity V of the vehicle. It may optionallyalso depend on the torque exerted by the driver on the steering wheel.

The fourth constraint Z9, which is applied to the amplitude-saturatedyaw-moment setpoint M_(z_ref), is a velocity saturation. It is moreprecisely a limitation of the rate of variation of the yaw-momentsetpoint M_(z_ref). The yaw moment variation rate threshold used isdenoted ∇M_(z) ^(ctrl) (it will also appear with the simplified notation∇).

This fourth constraint, by virtue of a controller K_(Brake), makes itpossible to obtain a braking torque to be provided to the actuators 32of the differential-braking system.

This fourth constraint is considered to be preferable in order toimprove the controllability of the vehicle when turning off or resumingthe yaw-moment setpoint M_(z_ref).

The block Z11 illustrates a second mechanism for inhibiting theregulation of the yaw-moment setpoint M_(z_ref). This second mechanismis intended to block the regulation and therefore the calculation of anydifferential engine torque, when the absolute value of the torqueexerted by the driver on the steering wheel exceeds a threshold denotedT_(Driver_Mz) ^(ctrl).

The aforementioned thresholds υ, T_(EPS_saturation_1) and ∇_(Mz) ^(ctrl)are obtained by carrying out road trials with the aid of a test vehicleof the same model as the vehicles on which the invention will beimplemented.

In particular, the threshold T_(EPS_saturation_1) is obtained fordifferent velocities V of the vehicle since it varies as a function ofthis parameter. It is obtained by carrying out trials while thedifferential-braking function is deactivated.

Likewise, the thresholds υ and ∇_(Mz) ^(ctrl) are obtained by means ofroad trials for different velocities V of the vehicle since they vary asa function of this parameter.

The limit M_(z_max) is for its part obtained in a particular way, withthe aid of the block Z10.

This limit is selected to be equal to a variable, denoted M _(z)^(ctrl), if the yaw velocity r of the vehicle exceeds in absolute valuea yaw velocity threshold which will be denoted here as r^(ctrl). Thelimit M_(z_max) will otherwise be selected to be equal to zero.

This may be written in the form of the following equation Math1:

$\begin{matrix}{M_{z\_{math}} = \left\{ \begin{matrix}{\overset{\_}{M}}_{z}^{ctrl} & {{{if}{❘r❘}} \geq {\overset{\_}{r}}^{ctrl}} \\0 & {else}\end{matrix} \right.} & \left\lbrack {{Math}.1} \right\rbrack\end{matrix}$

It may also be represented graphically, as shown by the part W1 of FIG.4 .

The yaw velocity threshold r^(ctrl) corresponds to the maximum yawvelocity at which the vehicle is still controllable by the driver, at agiven velocity V.

The yaw velocity threshold r^(ctrl) and the variable M _(z) ^(ctrl) areeither determined by trials of the test vehicle or calculated, or arecalculated then adjusted by means of trials. It is the first solutionthat is applied here.

For this purpose, during a first step, the differential-braking functionof the test vehicle is deactivated then controllability trials of thevehicle are carried out in order to determine the thresholds usable forthe constraints Z5 and Z7.

Next, during a second step, the differential-braking function of thevehicle is reactivated then new controllability trials are carried outin order to determine the maximum steering angle thresholds δ_(max)(V)for a plurality of different velocities (for example with an incrementof 5 km/h). As a variant, these steering angle thresholds could beobtained by calculation.

Finally, during a third step, the yaw velocity threshold r^(ctrl) andthe variable M _(z) ^(ctrl) are deduced therefrom.

The yaw velocity threshold r^(ctrl) is more precisely obtained bymodeling the vehicle by means of a bicycle model (described in moredetail below), then by deducing the following equation therefrom:

$\begin{matrix}{{{\overset{\_}{r}}^{ctrl}(V)} = {\frac{\left( {l_{f} + l_{r}} \right)V}{\left( {l_{f} + l_{r}} \right)^{2} + {k.V^{2}}}{\delta_{\max}(V)}}} & \left\lbrack {{Math}.2} \right\rbrack\end{matrix}$

In this equation, k is the understeer gradient, which is calculated bymeans of the following equation:

$\begin{matrix}{k = {m\left( {\frac{l_{r}}{C_{f}} - \frac{l_{f}}{C_{r}}} \right)}} & \left\lbrack {{Math}.3} \right\rbrack\end{matrix}$

By virtue of the same modeling, it is possible to obtain the variableM_(z) ^(ctrl) by means of the following equation:

$\begin{matrix}{{{\overset{¯}{M}}_{z}^{ctrl}(V)} = {\frac{C_{f}{C_{r}\left( {l_{f} + l_{r}} \right)}}{\left( {C_{f} + C_{r}} \right)}{\delta_{\max}(V)}}} & \left\lbrack {{Math}.4} \right\rbrack\end{matrix}$

The two inhibition mechanisms represented in FIG. 6 by the blocks Z6 andZ11 may now be addressed. These two mechanisms each involve a thresholdT_(Driver_δ) ^(ctrl), T_(Driver_Mz) ^(ctrl).

The threshold T_(Driver_δ) ^(ctrl) used to negate the steering-anglesetpoint δ_(ref) is determined by controllability trials carried out onthe vehicle when the differential-braking function is deactivated. Thisthreshold varies as a function of the velocity V of the vehicle.

The threshold T_(Driver_Mz) ^(ctrl) used to negate the yaw-momentsetpoint M_(z_ref) is determined by controllability trials when thedifferential-braking system is active. This threshold also varies as afunction of the velocity V of the vehicle.

It may be noted that these thresholds satisfy the following inequality:

T _(Driver_Mz) ^(ctrl)(V)≤T _(Driver_Saturation_1) ^(ctrl)(V)≤T_(Driver_δ) ^(ctrl)(V)  [Math. 5]

In this inequality, the variable T_(Driver_Saturation_1) ^(ctrl) isobtained from the threshold T_(EPS_Saturation_1). For this purpose,taking into account the function f corresponding to the assistance lawof the assisted-steering actuator 31, the following may be written:

T _(Driver_Saturation_1) ^(ctrl)(V)=f ⁻¹(T _(EPS_Saturation_1),V)  [Math. 6]

At this stage of the description, the procedure making it possible toobtain the values of the aforementioned thresholds and variables inorder to guarantee controllability of the vehicle may be summarized byusing FIG. 5 .

As this figure shows, during a first step E1, while thedifferential-braking function of the test vehicle is deactivated,controllability trials are performed in order to obtain the values ofthe thresholds T_(EPS_Saturation_1) and T_(Driver_δ) ^(ctrl).

Next, during a second step E2, the differential-braking function beingreactivated, a new series of controllability trials is performed inorder to obtain the values of the maximum steering angles δ_(max).

In this step, the value of the threshold T_(Driver_Saturation_1) ^(ctrl)is also calculated.

During a third step E3, the thresholds M _(z) ^(ctrl) and r ^(ctrl) arecalculated while taking into account the maximum steering anglesδ_(max).

Finally, during a fourth step E4, the results of the controllabilitytrials are used in order to refine the values of the thresholds M _(z)^(ctrl), r ^(ctrl) and in order to determine the values of the threshold∇_(Mz) ^(ctrl) and of the threshold of the driver torque T_(Driver_Mz)^(ctrl).

The various constraints mentioned above, and the way in which the choicebetween the steering angle of the steering wheel and thedifferential-braking system is made in order to pilot the vehicle, maynow be formulated.

For this purpose, reference may be made to the left part X1 of FIG. 6 .

In this figure, the block Z1 corresponds to the block that makes itpossible to determine the trajectory to be followed in order to avoidthe obstacle 20. Since the way in which this trajectory is determineddoes not form part of the subject matter of the present invention, itwill not be described here. This block Z1 then makes it possible, whenthe AES function is activated, to determine the lateral deviationsetpoint y_(L-ref) and the relative heading angle LPL.

The block Z2 is the one that makes it possible to make a choice betweenthe steering system and the differential-braking system in order tofollow the evasion trajectory optimally. It makes it possible todetermine the value of a coefficient α_(DB) that illustrates theproportion of the differential braking and of the steering angle whichis to be applied. When its value is zero, the differential braking isdeactivated, and when its value is maximum (equal to 1), it is thesteering angle that is deactivated. This block will be described indetail below.

The block Z3 corresponds to the mathematical function that makes itpossible to model the aforementioned constraints Z5 and Z7. It receivesas input the non-saturated steering-angle setpoint δ_(K).

The block Z4 corresponds to the mathematical function that makes itpossible to model the aforementioned constraints Z8 and Z9. It receivesas input the non-saturated yaw-moment setpoint M_(Kz).

These non-saturated setpoints are obtained with the aid of controllersdenoted K_(δ) for the calculation of the non-saturated steering-anglesetpoint δ_(K), and K_(M) for the calculation of the non-saturatedyaw-moment setpoint M_(Kz). They depend on the coefficient α_(DB).

In order to understand the calculations underlying these two blocks, itmay be assumed that the dynamic behavior of the vehicle can be modeledby means of the following equation Math7.

$\begin{matrix}{\begin{pmatrix}\beta \\\overset{.}{r} \\{\overset{.}{\psi}}_{L} \\{\overset{.}{e}}_{y_{L}} \\\overset{¨}{\delta} \\\overset{.}{\delta} \\{\overset{¨}{y}}_{L\_{ref}}\end{pmatrix} = \text{ }{{\begin{bmatrix}{- \frac{C_{f} + C_{r}}{mV}} & {1 + \frac{{C_{r}l_{r}} - {C_{f}l_{f}}}{{mV}^{2}}} & 0 & 0 & 0 & \frac{C_{f}}{mV} & 0 \\{- \frac{{C_{f}l_{f}} - {C_{r}l_{r}}}{J}} & {- \frac{{C_{r}l_{r}^{2}} - {C_{f}l_{f}^{2}}}{JV}} & 0 & 0 & 0 & \frac{C_{f}l_{f}}{J} & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\V & l_{s} & V & 0 & 0 & 0 & {- 1} \\0 & 0 & 0 & 0 & {{- 2}{\xi\omega}} & {- \omega^{2}} & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {- \omega_{f}}\end{bmatrix}\begin{pmatrix}\beta \\r \\\psi_{L} \\e_{y_{L}} \\\overset{.}{\delta} \\\delta \\{\overset{¨}{y}}_{L\_{ref}}\end{pmatrix}} + {\begin{bmatrix}0 \\0 \\0 \\0 \\\omega^{2} \\0 \\0\end{bmatrix}\delta_{ref}} + {\begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\\omega_{f}\end{bmatrix}w}}} & \left\lbrack {{Math}7} \right\rbrack\end{matrix}$

This model is an improved bicycle model.

But it does not thereby make it possible to limit the steering-angleamplitude and velocity of the front wheels 11 of the vehicle, or thedifferential-braking moment applied to the wheels of the vehicle, or thevariation of this braking moment. However, these limitations proveparticularly important for ensuring that the driver of the vehicle canbe capable of resuming control of the vehicle at any moment.

The saturation of the steering-angle velocity may be formulated in thefollowing way:

|{dot over (δ)}_(ref)|≤υ

In this equation Math 8, the threshold υ is for example equal to 0.0491rad/s, which corresponds to 0.785 rad/s at the steering wheel (i.e.45°/s) if the gear reduction coefficient of the steering is equal to 16.

As shown by FIG. 3 , the steering-angle velocity limiter is noteworthyinsofar as it forms a closed-loop pseudo-controller (that is to say acontroller carrying out simple and limited calculations), which has:

-   -   a direct-chain transfer function equal to the product of the        threshold υ (in order to comply with the condition stipulated by        the equation Math 8), a 1/s integrator and a corrector, which is        a function of the hyperbolic tangent type of Δ·α,    -   an indirect-chain (or “feedback-chain”) transfer function equal        to one.

A function of the hyperbolic tangent type is intended to mean thevarious functions that have a form similar to the hyperbolic tangentfunction, which includes in particular inverse trigonometric functions(such as the arctangent), the error function (commonly denoted erf), theGudermannian function (commonly denoted gd) and the hyperbolictrigonometric function (such as hyperbolic tangent).

It receives as input the non-saturated steering-angle setpoint δ_(ref)and transmits as output the saturated steering-angle setpoint δ_(ref).

In this figure, the coefficient Δ corresponds to the deviation betweenthe variables δ_(K) and δ_(ref). The coefficient α is a constant between0 and infinity, which is the only parameter making it possible to affectthe rapid or flexible nature of the steering-angle limiter.

This steering-angle velocity limiter thus has the advantage of beingsimple to tune, since it is sufficient to adjust the coefficient α. Itmakes it possible to ensure continuous and smooth (infinitelydifferentiable) command.

For this purpose, taking into account the form of this steering-anglevelocity limiter L2, the following equation Math9 may be written:

{dot over (δ)}_(ref)=υ·tanh(∝(δ_(K)−δ_(ref)))  [Math 9]

A controllability model of the vehicle is thus obtained which ispseudo-linear.

More precisely, the following parameter es may then be introduced:

$\begin{matrix}{\theta_{\delta} = \frac{\tanh\left( {\propto {.\left( {\delta_{K} - \delta_{ref}} \right)}} \right)}{\propto {.\left( {\delta_{K} - \delta_{ref}} \right)}}} & \left\lbrack {{Math}10} \right\rbrack\end{matrix}$

and then the equation Math 10 may be rewritten in the form:

{dot over (δ)}_(ref)=−υ·α·θ_(δ)·δ_(ref)+υ·α·θ_(δ)·δ_(K)  [Math 11]

This equation Math 11 is characteristic of a state representation, andit shows that the setpoint variation limiting model is linear as afunction of the parameter es.

On this basis, it is then possible to determine the controller whichensures good following of the evasion trajectory T0, which satisfies thesetpoint variation limiting model and which complies with the conditionstipulated by the coefficient α_(DB).

The saturation of the yaw-moment setpoint M_(z_ref) may be formulated inthe following way:

|M _(z_ref) |≤M _(z_max)  [Math 12]

The saturation of the rate of variation of the yaw-moment setpointM_(z_ref) may be formulated in the following way:

|{dot over (M)} _(z_ref)|≤∇_(Mz) ^(ctrl)  [Math 13]

According to the invention, the amplitude and the rate of variation ofthe yaw-moment setpoint M_(z_ref) are intended to be limited not byimposing a severe threshold, but instead by using a setpoint amplitudelimiter and a setpoint variation limiter.

Referring to FIG. 4 , the amplitude limiter that will be used here tomodify the non-saturated yaw-moment setpoint M_(Kz), in order togenerate a semi-saturated yaw-moment setpoint M_(z_sat), may first bedescribed.

This amplitude limiter is noteworthy insofar as it forms a closed-looppseudo-controller which has:

-   -   a direct-chain transfer function equal to the product of the        limit M_(z_max) (in order to comply with the condition        stipulated by the equation Math 12) and a corrector, which is a        function of the hyperbolic tangent type of β₁·ε₁,    -   an indirect-chain (or “feedback-chain”) transfer function equal        to one.

In this FIG. 4 , the coefficient ε₁ corresponds to the deviation betweenthe variables M_(z_sat) and M_(Kz). The coefficient β₁ is a constantbetween 0 and infinity, which is the one and only parameter making itpossible to affect the rapid or flexible nature of the amplitudelimiter.

The use of such a pseudo-controller makes it possible not only totime-limit the yaw-moment setpoint M_(z_ref) well, but furthermore toensure continuity of the variation of this setpoint.

Taking into account the form of this amplitude limiter, the equationMath14 may be written:

M _(z_sat) =M _(z_max)·tanh(β₁·(M _(z_sat) −M _(Kz)))  [Math 14]

As shown by FIG. 4 , the rate of variation limiter of the yaw moment isalso noteworthy in that it forms a closed-loop pseudo-controller, whichhas:

-   -   a direct-chain transfer function equal to the product of the        constant ∇_(Mz) ^(ctrl) (in order to comply with the condition        stipulated by the equation Math 13), a 1/s integrator and a        corrector, which is a function of the hyperbolic tangent type of        β₂·ε₂,    -   an indirect-chain (or “feedback-chain”) transfer function equal        to one.

It receives as input the semi-saturated yaw-moment setpoint M_(z_sat)and transmits as output the yaw-moment setpoint M_(z_ref).

In this figure, the coefficient ε₂ corresponds to the deviation betweenthe variables M_(z_ref) and M_(z_sat). The coefficient β₂ is a constantbetween 0 and infinity, which is the only parameter making it possibleto affect the rapid or flexible nature of the velocity limiter.

The use of such a corrector makes it possible not only to time-limit theyaw-moment variations well, but furthermore to ensure continuity of thisvariation.

Taking into account the form of this velocity limiter, the equationMath15 may be written:

{dot over (M)} _(z_ref)=∇_(Mz) ^(ctrl)·tanh(ε₂(M _(z_sat) −M_(z_ref)))  [Math 15]

A controllability model of the vehicle is thus obtained which ispseudo-linear.

Some variables may now be introduced to simplify the expressions ofequations Math 14 and Math 15, in order to represent the full modelquasi-linearly (that is to say in the manner of LPV, Linear ParameterVarying), in the form of a state representation.

The equation Math 14 may be written in the form of an equation Math16:

$\begin{matrix}{M_{z_{sat}} = {{M_{z\_\max} \cdot \beta_{1} \cdot \left( {M_{z_{sat}} - M_{Kz}} \right)}\rho}} & \left\lbrack {{Math}16} \right\rbrack\end{matrix}$ with $\begin{matrix}{\rho = \frac{tan{h\left( {\beta_{1}\left( {M_{zK} - M_{z{\_{sat}}}} \right)} \right)}}{\beta_{1}\left( {M_{zK} - M_{z{\_{sat}}}} \right)}} & \left\lbrack {{Math}17} \right\rbrack\end{matrix}$

The following parameter θ_(Δ) may then be introduced:

$\begin{matrix}{\theta_{\Delta} = {\frac{\rho}{1 + {\Delta\beta_{1}\rho}}\frac{\Delta}{{\overset{¯}{M}}_{z}^{ctrl}}}} & \left\lbrack {{Math}18} \right\rbrack\end{matrix}$

Next, the equation Math 15 may be rewritten in the form of an equationMath19:

$\begin{matrix}{{\overset{˙}{M}}_{z\_{ref}} = {{{- a_{1}}\theta_{\nabla}M_{z\_{ref}}} + {a_{2}\theta_{\nabla\Delta}M_{zK}}}} & \left\lbrack {{Math}19} \right\rbrack\end{matrix}$ with $\begin{matrix}{a_{1} = {\nabla\beta_{2}}} & \left\lbrack {{Math}20} \right\rbrack\end{matrix}$ $\begin{matrix}{a_{2} = {{\nabla{\overset{¯}{M}}_{z}}\beta_{1}\beta_{2}}} & \left\lbrack {{Math}21} \right\rbrack\end{matrix}$ $\begin{matrix}{\theta_{\nabla\Delta} = {\theta_{\nabla}\theta_{\Delta}}} & \left\lbrack {{Math}22} \right\rbrack\end{matrix}$ $\begin{matrix}{\theta_{\nabla} = \frac{tan{h\left( {\beta_{2}\left( {M_{z{\_{sat}}} - M_{z\_{ref}}} \right)} \right)}}{\beta_{2}\left( {M_{z{\_{sat}}} - M_{z\_{ref}}} \right)}} & \left\lbrack {{Math}23} \right\rbrack\end{matrix}$

The equation Math 19 is characteristic of a state representation, and itshows that the full yaw-moment amplitude and velocity limiting model isquasi-linear as a function of the exogenous parameters θ_(∇Δ) and θ_(∇)(parameters which can be calculated when the vehicle is in motion).

The bicycle model of equation Math 7 may then be enhanced with thisstate representation in order to obtain a new usable model.

In this way, it is possible to synthesize the controllers (representedin FIG. 6 by K_(δ), K_(M) and by the blocks Z3 and Z4) by anoptimization method such as that of linear matrix inequalities.

These controllers may then be implemented in the computers 13 of motorvehicles 10 of the production series of the motor vehicle on which thetrials were carried out.

By way of example, the way in which the synthesis of the firstcontroller (the one that makes it possible to obtain the steering-anglesetpoint δ_(ref)) is carried out may be described. The synthesis of thesecond controller (the one that makes it possible to obtain theyaw-moment setpoint) will be performed in a corresponding way, and willtherefore not be described in detail here.

The enhanced bicycle model of equation Math 7 is written:

[Math24] $\begin{pmatrix}\beta \\\overset{.}{r} \\{\overset{.}{\psi}}_{L} \\{\overset{.}{e}}_{y_{L}} \\\overset{¨}{\delta} \\\overset{.}{\delta} \\\begin{matrix}{\overset{¨}{y}}_{L\_{ref}} \\{\overset{.}{\delta}}_{ref}\end{matrix}\end{pmatrix} = \text{ }{{\begin{bmatrix}{- \frac{C_{f} + C_{r}}{mV}} & {1 + \frac{{C_{r}l_{r}} - {C_{f}l_{f}}}{{mV}^{2}}} & 0 & 0 & 0 & \frac{C_{f}}{mV} & 0 & 0 \\{- \frac{{C_{f}l_{f}} - {C_{r}l_{r}}}{J}} & {- \frac{{C_{r}l_{r}^{2}} - {C_{f}l_{f}^{2}}}{JV}} & 0 & 0 & 0 & \frac{C_{f}l_{f}}{J} & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\V & l_{s} & V & 0 & 0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 0 & {{- 2}{\xi\omega}} & {- \omega^{2}} & 0 & \omega^{2} \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {- \omega_{f}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {{- {va}}\theta_{2}}\end{bmatrix}\begin{pmatrix}\beta \\r \\\psi_{L} \\e_{y_{L}} \\\overset{.}{\delta} \\\delta \\\begin{matrix}{\overset{.}{y}}_{L\_{ref}} \\\delta_{ref}\end{matrix}\end{pmatrix}} + {\begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\\begin{matrix}0 \\{{va}\theta_{2}}\end{matrix}\end{bmatrix}\delta_{K}} + {\begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\\begin{matrix}\omega_{f} \\0\end{matrix}\end{bmatrix}w}}$

A state vector x may then be considered, which can be written in theform:

x=(βrΨ _(L) e _(y) _(L) {dot over (δ)}δ{dot over (y)}_(L_ref)δ_(ref))^(T)  [Math 25]

The aim is then to determine the form of the controller Ks which is thestate feedback making it possible to calculate the non-saturatedsteering-angle setpoint δ_(K) on the basis of this state vector x.

In order to understand how to determine a controller Ks that is suitablein terms of both stability and rapidity, our behavioral model may now bewritten in a generic form:

$\begin{matrix}\left\{ \begin{matrix}\overset{.}{x} & {= {{{A\left( \theta_{\delta} \right)}x} + {{B_{u}\left( \theta_{\delta} \right)}.\delta_{ref}} + {B_{w}w}}} \\y & {= {C_{y}.x}}\end{matrix} \right. & \left\lbrack {{Math}26} \right\rbrack\end{matrix}$

In this equation, C_(y) is the identity matrix, A is a dynamic matrix,B_(u) is a command matrix and B_(w) is a perturbation matrix, which maybe written in the form:

[Math27] ${A = \text{ }\begin{bmatrix}{- \frac{C_{f} + C_{r}}{mV}} & {1 + \frac{{C_{r}l_{r}} - {C_{f}l_{f}}}{{mV}^{2}}} & 0 & 0 & 0 & \frac{C_{f}}{mV} & 0 & 0 \\{- \frac{\left( {{C_{f}l_{f}} - {C_{r}l_{r}}} \right)}{(J)}} & {- \frac{\left( {{C_{r}l_{r}^{2}} - {C_{f}l_{f}^{2}}} \right)}{({JV})}} & 0 & 0 & 0 & \frac{C_{f}l_{f}}{J} & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\V & l_{s} & V & 0 & 0 & 0 & {- 1} & 0 \\0 & 0 & 0 & 0 & {{- 2}{\xi\omega}} & {- \omega^{2}} & 0 & \omega^{2} \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {- \omega_{f}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 & {{- {va}}\theta_{2}}\end{bmatrix}},$ ${B_{u} = \begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\\begin{matrix}0 \\{{va}\theta_{2}}\end{matrix}\end{bmatrix}},{B_{w} = \begin{bmatrix}0 \\0 \\0 \\0 \\0 \\0 \\\begin{matrix}\omega_{f} \\0\end{matrix}\end{bmatrix}},$

The controller K_(δ), which is defined as a static state feedback, mayfor its part be expressed in the form:

δ_(K) =K _(δ) ·x  [Math 28]

In order to find an optimal controller K_(δ), various methods may beused.

The method used here is that of linear matrix inequalities. It is thuscarried out on the basis of convex-optimization criteria underconstraints of linear matrix inequalities.

The aim is more precisely to optimize the gains of the closed loopdefined by the controller K_(δ) by varying on the choice of the poles.

Three matrix inequalities are used, and these are defined by thefollowing inequalities.

$\begin{matrix}{{{A_{\overset{˙}{í}}Q} + {B_{i}R} + \left( {{A_{i}Q} + {B_{i}R}} \right)^{T} + {2\mu Q}} \prec 0} & \left\lbrack {{Math}29} \right\rbrack\end{matrix}$ $\begin{matrix}{\begin{bmatrix}{{- \gamma}Q} & {{A_{i}Q} + {B_{i}R}} \\* & {{- \gamma}Q}\end{bmatrix} \prec 0} & \left\lbrack {{Math}30} \right\rbrack\end{matrix}$ $\begin{matrix}{\begin{bmatrix}\begin{matrix}{\sin(\varphi)\left( {{A_{i}Q} + {B_{i}R} +} \right.} \\\left. \left( {{A_{i}Q} + {B_{i}R}} \right)^{T} \right)\end{matrix} & \begin{matrix}{\cos(\varphi)\left( {{A_{i}Q} + {B_{i}R} -} \right.} \\\left. \left( {{A_{i}Q} + {B_{i}R}} \right)^{T} \right)\end{matrix} \\* & \begin{matrix}{{\sin(\varphi)}\left( {{A_{i}Q} + {B_{i}R} -} \right.} \\\left. \left( {{A_{i}Q} + {B_{i}R}} \right)^{T} \right)\end{matrix}\end{bmatrix} \prec 0} & \left\lbrack {{Math}31} \right\rbrack\end{matrix}$

In these inequalities, i is equal to 1 or 2, and the matrices A_(i) andB_(i) may then be defined in the following way:

A ₁ =A(θ_(δmin))

A ₂ =A(θ_(δmax))

B ₁ =B _(u)(θ_(δmin))

B ₂ =B _(u)(θ_(δmax))  [Math 32]

A matrix of the form

$\begin{bmatrix}X & Y \\Y^{T} & W\end{bmatrix}$

is written in the form

$\begin{bmatrix}X & Y \\* & W\end{bmatrix}.$

The controller K_(δ) is defined by the equation:

K _(δ) =R·Q ⁻¹  [Math 33]

The velocity of the vehicle is assumed to be constant (and all thematrices of the system are therefore deemed to be constant).

The three inequalities make it possible to ensure that the dynamics ofthe closed loop remain limited. This is because, by virtue of theseconstraints, the poles of the closed loop become bounded in a zonedefined by a radius γ, a minimum distance from the imaginary axis μ, andan aperture angle φ.

This method proves effective because it involves determining thesteering-wheel angle at each instant in a way which is reasonable (andcan be mastered by a driver with average competence) and in a way whichcan be performed by the actuator. These constraints also ensurestability of the closed loop.

The aim here is to minimize the radius γ. Once the controller K_(δ) hasbeen obtained, the non-saturated steering-angle setpoint may be obtainedcalculated by means of the following formula:

$\begin{matrix}{\delta_{K} = {{Kx} = {\begin{bmatrix}k_{\beta} & k_{r} & k_{\varphi_{L}} & k_{e_{y_{L}}} & k_{\overset{.}{\delta}} & k_{\delta} & k_{{\overset{.}{y}}_{L\_{ref}}} & k_{\delta_{ref}}\end{bmatrix}\begin{pmatrix}\beta \\r \\\psi_{L} \\e_{y_{L}} \\\overset{.}{\delta} \\\delta \\\begin{matrix}{\overset{.}{y}}_{L\_{ref}} \\\delta_{ref}\end{matrix}\end{pmatrix}}}} & \left\lbrack {{Math}33} \right\rbrack\end{matrix}$

The values θ_(δmin) and θ_(δmax) have been introduced into the threematrix inequalities.

The value of θ_(δ), which is linked to the deviation between δ_(K) andδ_(ref), reflects the level of violation by the controller Ks of thecontrollability limit set down by the equation Math 8.

By definition, θ_(δ) lies between 0 (exclusive) and 1 (inclusive). Whenθ_(δ) is equal to 1, the calculated non-saturated setpoint of the angleat the steering wheel δ_(K) complies well with the controllabilitylimit. When it is close to 0, the calculated non-saturated setpoint ofthe angle at the steering wheel δ_(K) has a value which imposes steeringdynamics that are too great, which generates a risk of instability ofthe vehicle. When θ_(δ) takes intermediate values between 0 and 1, thecontrollability limit is not complied with but it is possible for thereto be no risk of instability of the vehicle.

In other words, the choice of the values θ_(δmin) and θ_(δmax) has adirect impact on the performance and the robustness of the controllerKs. The larger the interval [θ_(δmin), θ_(δmax)] is, the less well thecontroller K_(δ) performs, but the more robust it is. Conversely, thesmaller this interval is, the better the controller K_(δ) performs butthe less robust it is.

Logically, the value θ_(δmax) is selected to be equal to 1 (a caseaccording to which the controller K_(δ) functions in linear mode, as ismoreover generally the case, without controllability constraintviolation).

The determination of the value θ_(δmin), on the other hand, requiresmaking a compromise between performance and robustness. Thedetermination of this value equates to imposing a maximum threshold forthe deviation, in absolute value, between δ_(K) and δ_(ref).

In summary, the method for calculating the controller Ks that issuitable for a particular motor vehicle model consists in fixing onvalues of α_(DB), v, α, θ_(δmin) and θ_(δmax).

It next consists in determining the coefficients of the matrices A_(i),B_(i), then in solving the equations Math 29 to Math 31 in order todeduce therefrom a controller K_(δ) that ensures good following of theevasion trajectory T0 and satisfies the steering-angle setpointvariation limiting model.

The block Z2 may now be described in more detail.

The way in which the coefficient α_(DB) is obtained, which it will berecalled illustrates the proportion of differential braking and steeringangle to be applied, may now be described.

For this purpose, a preliminary variable α_(DB_raw) is initiallyselected.

This choice is made only if the torque exerted by the driver on thesteering wheel is less than or equal to, in absolute value, thethreshold T_(Driver_Mz) ^(ctrl).

Specifically, if it is greater than this threshold, no setpoint will becalculated.

In the case in which it is less than or equal to the thresholdT_(Driver_Mz) ^(ctrl), the preliminary variable α_(DB_raw) is selectedto be equal to 1 if the two following cumulative conditions arefulfilled. Otherwise, it is selected to be equal to zero.

The first condition is that the variable θ_(δ), in absolute value, isless than or equal to a variable θ_(δ) ^(min) in absolute value.

This variable θ_(δ) ^(min) is the minimum value of the variable θ_(δ) atwhich the steering-angle controller K_(δ) on its own can stabilize thevehicle. It is a variable since it depends on the velocity V of thevehicle.

In other words, the first condition consists in checking whether or notthe steering-angle setpoint is saturated.

The second condition is that the yaw velocity is less than or equal to,in absolute value, the yaw velocity threshold r^(ctrl) in absolutevalue.

Once the value (0 or 1) of the preliminary variable α_(DB_raw) has beenchosen, it is possible to calculate the coefficient α_(DB) by means ofthe following equation:

$\begin{matrix}{\alpha_{DB} = {\frac{\tau_{DB}}{s + \tau_{DB}}\alpha_{{DB}\_{raw}}}} & \left\lbrack {{Math}24} \right\rbrack\end{matrix}$

In this equation, the parameter τ_(DB) is a time constant that makes itpossible to filter any abrupt change of the coefficient α_(DB) in orderto guarantee a good feel for the driver. The value of this parameter istherefore adjustable according to the feel that the driver wishes tohave.

The parameters is the Laplace variable.

At this stage, the process that will be executed by the computer 13 ofone of the motor vehicles of the aforementioned production series, inorder to carry out the invention, may be described.

Here, the computer 13 is programmed in order to carry out this processrecursively, that is to say step-by-step, and in a loop.

For this purpose, during a first step, the computer 13 checks that theautomatic obstacle evasion function (AES) is activated.

If this is the case, it attempts to detect the presence of a possibleobstacle lying on the path of the motor vehicle 10. For this purpose, ituses its RADAR or LIDAR remote detector.

In the absence of an obstacle, this step is repeated in loops.

As soon as an obstacle 20 is detected (see FIG. 2 ), the computer 13plans an evasion trajectory T0 making it possible to avoid this obstacle20.

The computer 13 will then try to define piloting setpoints for theconventional steering system and for the differential-braking system,which make it possible to follow this evasion trajectory T0 optimally.

For this purpose, it starts by calculating or measuring parameters,these parameters characterizing in particular the dynamic behavior ofthe vehicle, such as:

-   -   the measured steering angle δ,    -   the time derivative of the measured steering angle δ,        -   the saturated steering-angle setpoint δ_(ref) obtained in            the preceding time increment,    -   the yaw velocity r,    -   the relative heading angle Ψ_(L),    -   the time derivative of the lateral deviation setpoint y_(L-ref),    -   the trajectory following error e_(yL),    -   the drift angle β,    -   the coefficient α_(DB).

As shown by FIG. 6 , the computer 13 next uses the controllers K_(δ) andK_(M) stored in its memory. These controllers will therefore make itpossible to determine the values of the non-saturated steering-anglesetpoint δ_(K) and non-saturated yaw angle setpoint M_(Kz).

The pseudo-controllers represented in FIG. 6 by the blocks Z3 and Z4will next make it possible to deduce therefrom the saturated setpointsof steering angle δ_(ref) and yaw moment M_(z_ref). These setpoints willthen be transmitted to the actuators 31, 32 in order to divert thevehicle from its initial trajectory.

In other words, it is therefore the combination of the controller K_(δ)and the pseudo-controller represented by the block Z3 which will form afirst overall controller making it possible to determine thesteering-angle setpoint δ_(ref) on the basis of the parameters listedabove.

Likewise, it is the combination of the controller K_(M) and thepseudo-controller represented by the block Z4 which will form a secondoverall controller making it possible to determine the yaw-momentsetpoint M_(z_ref) on the basis of the parameters listed above.

The present invention is in no way limited to the embodiment described.Rather, a person skilled in the art will know how to add thereto anyvariant according to the invention.

1-11. (canceled)
 12. A process for automated piloting of a motor vehiclehaving wheels, at least two of the wheels being steered wheels, themethod comprising: acquiring parameters relating to a trajectory for themotor vehicle to avoid an obstacle; and calculating by a computer afirst piloting setpoint of a steering-angle actuator of the steeredwheels and a second piloting setpoint of at least onedifferential-braking actuator of the wheels, as a function of saidparameters, wherein the first piloting setpoint and the second pilotingsetpoint are each determined by a controller that satisfies a setpointamplitude and/or variation limiting model, and wherein the firstpiloting setpoint and the second piloting setpoint are determined as afunction of a coefficient that fixes a contribution of each actuator,said coefficient being calculated as a function of a yaw velocity of themotor vehicle, a torque applied by a driver to a steering wheel of themotor vehicle and a parameter, the value of which varies according towhether or not the first piloting setpoint is limited by the controller.13. The process as claimed in claim 12, wherein the first pilotingsetpoint and/or the second piloting setpoint is determined by acontroller that satisfies a setpoint amplitude and variation limitingmodel.
 14. The process as claimed in claim 12, wherein the coefficientis calculated so that: the second piloting setpoint is zero when theabsolute value of the torque applied by the driver to the steering wheelof the motor vehicle exceeds a predetermined threshold, only thesteering-angle actuator of the steered wheels is used when the yawvelocity of the vehicle is greater than a control threshold and/or whenthe piloting setpoint on its own makes it possible to stabilize themotor vehicle, and otherwise, the steering-angle actuator of the steeredwheels and the differential-braking actuator of the wheels are used incombination.
 15. The process as claimed in claim 14, wherein thecoefficient is calculated so as to vary continuously as a function oftime.
 16. The process as claimed in claim 12, further comprisinginterrupting the determination of the first piloting setpoint when theabsolute value of the torque applied by the driver to the steering wheelof the motor vehicle exceeds a predetermined threshold.
 17. The processas claimed in claim 12, further comprising interrupting thedetermination of the second piloting setpoint when the absolute value ofthe torque applied by the driver to the steering wheel of the motorvehicle exceeds a predetermined threshold.
 18. The process as claimed inclaim 12, wherein the controller making it possible to determine thesecond piloting setpoint satisfies an amplitude limiting model, so thatthe second piloting setpoint remains less than or equal to a limit, andwherein said limit is determined as a function of a velocity and the yawvelocity of the motor vehicle.
 19. The process as claimed in claim 12,wherein, in order to calculate the first piloting setpoint, provision ismade to determine a first non-saturated setpoint and to deduce the firstsetpoint therefrom by a closed-loop pseudo-controller having adirect-chain transfer function that comprises a function of thehyperbolic tangent type of the deviation between the first non-saturatedsetpoint and the first setpoint.
 20. The process as claimed in claim 12,wherein, in order to calculate the second setpoint, provision is made:to determine a second non-saturated setpoint and to deduce a secondsemi-saturated setpoint therefrom by a closed-loop pseudo-controllerhaving a direct-chain transfer function that comprises a function of thehyperbolic tangent type of the deviation between the secondnon-saturated setpoint and the second semi-saturated setpoint, then touse another closed-loop pseudo-controller, which provides the secondsetpoint as output and the direct-chain transfer function of whichcomprises a function of the hyperbolic tangent type of the deviationbetween the second semi-saturated setpoint and said second setpoint. 21.A method for creating controllers for the process as claimed in claim12, the method comprising: acquiring a behavioral matrix model of theapparatus; determining at least some of the coefficients of matrices ofthe behavioral matrix model; deducing two controllers therefrom, each ofwhich satisfies a piloting setpoint amplitude limiting model and/or apiloting setpoint variation limiting model.
 22. A motor vehiclecomprising: a steering-angle actuator of the steered wheels, adifferential-braking actuator of the steered wheels, and a computerconfigured to pilot said actuators, wherein the computer is programmedin order to carry out the process as claimed in claim 12.